The ubiquitous traction force pattern generated by a single polarized cell with a long axis \({\mathbf {a}}\)  and exerting a typical force \(\mathbf {F}\)  at its adhesions, can be modeled as a force dipole, \(P_{ij} = F_{i} a_{j}\)  ([fig:MasterPlot2]Fig. 1 d). The resulting deformation in the elastic substrate is given by the strain, \(u_{ij}\) , which is determined by a force balance in linear elastic theory (see SI section A), and depends on the material properties of the elastic medium, specifically, the stiffness or Young's modulus \(E\) , and the compressibility, given by the Poisson's ratio \(\nu \)  [1]}. The substrate deformation (\(u_{xx}\)  component of strain) generated by a dipole (oriented along the laboratory \(x-\) axis) embedded on the surface of a linear elastic medium is shown in ([fig:MasterPlot2]Fig. 1 e)) for two representative values of \(\nu \) . Here, the blue (red) coloring represents expanded (compressed) regions of the substrate.
